Characterization of Solitary Waves in Fermi-Pasta-Ulam-Tsingou systems
MetadataShow full item record
It is well known that a velocity perturbation can travel through a mass spring chain with quadratic + quartic interactions as a solitary and antisolitary wave pair. In this thesis we will characterize traveling waves on a Fermi-Pasta-Ulam-Tsingou (FPUT) chain. We show the existence of solitary wave solutions and characterize the solitary wave's width, height and speed. Using the Virial theorem we show that the FPUT chain be related to an effective Hertzian system. Next we study how solitary waves interact with one another on a FPUT chain. We examine the resulting dynamics and study whether or not solitary waves can break and reform. In addition we study the interacting of solitary waves and anti-solitary waves. We investigate the creation of long lived localized oscillations that can be created from solitary wave anti-solitary wave interactions. In recent years, nonlinear wave propagation in 2 D structures have also been explored. In this thesis we consider the propagation of such a velocity perturbation through systems having a 2 D "Y" shaped structure where each of the three pieces that make up the "Y" are made of a small mass spring chain. In addition, we consider the case where multiple "Y" shaped structures are used to generate a "tree". Lastly we layout the study of the properties of 2 D structures that are not constrained to an explicit shape. We allow these systems to evolve and adapt as energy passes through them and study the ultimate shapes they form as a result of external perturbations.